Find x and y. please help !

Kesha rode her bike 12 miles from home to the store. She rode her bike back towards home from the store for 8 miles then walked

stellarik [79]

Answer:

0 Kesha is already home 8+4 is 12 and it's 12 miles from the store to her house .-.

Step-by-step explanation:

5 0

3 years ago

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Assume that all six outcomes of a six-sided number cube have the same probability. What is the theoretical probability of each r

Margarita [4]

Hey there! I am on the same one. :) I will help you out a little.

Assume that all six outcomes of a six-sided number cube have the same probability. What is the theoretical probability of each roll?
• 1: 1/6
• 2: 2/6
• 3: 3/6
• 4: 4/6
• 5: 5/6
• 6: 6/6

Using the uniform probability model you developed, what is the probability of rolling an even number?
1/6 Roll a number cube 25 times. Record your results here.

 1st toss=6 2nd toss=4 3rd toss=6 4th toss=6 5th toss=3 6th toss=3 7th toss=4 8th toss=2 9th toss=6 10th toss=5 11th toss=1 12th toss=4 13th toss = 5 14th toss =1 15th toss=4 16th toss=2 17th toss=2 18th toss=2 19th toss=6 20th toss=5 21st toss=3 22nd toss=4 23rd toss=3 24th toss=3 25 toss=5
How many results of 1 did you have? __2____________ How many results of 2 did you have? ____4__________ How many results of 3 did you have? ____5__________ How many results of 4 did you have? ______5________ How many results of 5 did you have? ______4________ How many results of 6 did you have? ______5________
Based on your data, what is the experimental probability of each roll? 1. 2/25 or 0.08

2. 4/25 or 0.16

3. 5/25 or 0.24

4. 5/25 or 0.2

5.4/25 or 0.16

6. 5/25 or 0.2Using the probability model based on observed frequencies, what is the probability of rolling an even number? 3/6 = ½ or 0.5
Was your experimental probability different than your theoretical probability? Why or why not? It somewhat is! The denominator is 25 for the experimental probability, and 6 for the theoretical probability.
Have a lovely day! Cheerio. :)

8 0

3 years ago

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How can you tell if a point is a solution to a system of equations?

Anna35 [415]

Answer: you have to substitute them into the equation

Step-by-step explanation:

example: x = 2y - 6

lets say you test 4/5 so it would be 4 = 2(5) - 6

this equals 4 = 10 - 6 which is true

so that is how you test to see if the equation is right

remember the first number goes to "x" and the second one goes to y

hope this helps mark me brainliest if you can

3 0

3 years ago

1. The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base? Enter

Elodia [21]

Answers:
1. 8 m
2. 17 m
3. 7 cm
4. 2 s

Explanations:

1. Let x = length of the base
x + 6 = height of the base

Then, the area of the triangle is given by

(Area) = (1/2)(base)(height)
56 = (1/2)(x)(x + 6)
56 = (1/2)(x²  + 6x)

Using the symmetric property of equations, we can interchange both sides of equations so that

(1/2)(x²  + 6x) = 56

Multiplying both sides by 2, we have

x² + 6x = 112

The right side should be 0. So, by subtracting both sides by 112, we have

x² + 6x - 112 = 112 - 112
x² + 6x - 112 = 0

By factoring, x² + 6x - 112 = (x - 8)(x + 14). So, the previous equation becomes

(x - 8)(x +14) = 0

So, either

x - 8 = 0 or x + 14 = 0

Thus, x = 8 or x = -14. However, since x represents the length of the base and the length is always positive, it cannot be negative. Hence, x = 8. Therefore, the length of the base is 8 cm.

2. Let x = length of increase in both length and width of the rectangular garden

Then,

14 + x = length of the new rectangular garden
12 + x = width of the new rectangular garden

So,

(Area of the new garden) = (length of the new garden)(width of the new garden)

255 = (14 + x)(12 + x) (1)

Note that

(14 + x)(12 + x) = (x + 14)(x + 12)
= x(x + 14) + 12(x + 14)
= x² + 14x + 12x + 168
= x² + 26x + 168

So, the equation (1) becomes

255 = x² + 26x + 168

By symmetric property of equations, we can interchange the side of the previous equation so that

x² + 26x + 168 = 255

To make the right side becomes 0, we subtract both sides by 255:

x² + 26x + 168 - 255 = 255 - 255
x² + 26x - 87 = 0

To solve the preceding equation, we use the quadratic formula.

First, we let

a = numerical coefficient of x² = 1

Note: if the numerical coefficient is hidden, it is automatically = 1.

b = numerical coefficient of x = 26
c = constant term = - 87

Then, using the quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{-26 \pm \sqrt{26^2 - 4(1)(-87)} }{2(1)} 
\newline x = \frac{-26 \pm \sqrt{1,024} }{2}
\newline
\newline x = \frac{-26 \pm 32 }{2}$

So,

$x = \frac{-26 + 32 }{2} \text{ or } x = \frac{-26 - 32 }{2}
\newline x = \frac{6 }{2} \text{ or } x = \frac{-58 }{2}
\newline \boxed{ x = 3 \text{ or } x = -29}$

Since x represents the amount of increase, x should be positive.

Hence x = 3.

Therefore, the length of the new garden is given by

14 + x = 14 + 3 = 17 m.

3. The area of the shaded region is given by

(Area of shaded region) = π(outer radius)² - π(inner radius)²
= π(2x)² - π6²
= π(4x² - 36)

Since the area of the shaded region is 160π square centimeters,

π(4x² - 36) = 160π

Dividing both sides by π, we have

4x² - 36 = 160

Note that this equation involves only x² and constants. In these types of equation we get rid of the constant term so that one side of the equation involves only x² so that we can solve the equation by getting the square root of both sides of the equation.

Adding both sides of the equation by 36, we have

4x² - 36 + 36 = 160 + 36
4x² = 196

Then, we divide both sides by 4 so that

x² = 49

Taking the square root of both sides, we have

$x = \pm 7$

Note: If we take the square root of both sides, we need to add the plus minus sign $(\pm)$ because equations involving x² always have 2 solutions.

So, x = 7 or x = -7.

But, x cannot be -7 because 2x represents the length of the outer radius and so x should be positive.

Hence x = 7 cm

4. At time t, h(t) represents the height of the object when it hits the ground. When the object hits the ground, its height is 0. So,

h(t) = 0 (1)

Moreover, since $v_0 = 27$ and $h_0 = 10$ ,

h(t) = -16t² + 27t + 10 (2)

Since the right side of the equations (1) and (2) are both equal to h(t), we can have

-16t² + 27t + 10 = 0

To solve this equation, we'll use the quadratic formula.

Note: If the right side of a quadratic equation is hard to factor into binomials, it is practical to solve the equation by quadratic formula.

First, we let

a = numerical coefficient of t² = -16
b = numerical coefficient of t = 27
c = constant term = 10

Then, using the quadratic formula

$t = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{-27 \pm \sqrt{27^2 - 4(-16)(10)} }{2(-16)} \newline t = \frac{-27 \pm \sqrt{1,369} }{-32} \newline \newline t = \frac{-27 \pm 37 }{32}$

So,

$t = \frac{-27 + 37 }{-32} \text{ or } t = \frac{-27 - 37 }{-32} \newline t = \frac{-10}{32} \text{ or } t = \frac{-64 }{-32} \newline \boxed{ t = -0.3125 \text{ or } t = 2}$

Since t represents the amount of time, t should be positive.

Hence t = 2. Therefore, it takes 2 seconds for the object to hit the ground.

3 0

3 years ago

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An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberr

seraphim [82]

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean compression strength from the extra carbonation of strawberry drink and μ2 be the mean compression strength from the extra carbonation of cola.

The random variable is μ1 - μ2 = difference in the mean compression strength from the extra carbonation of strawberry drink and the mean compression strength from the extra carbonation of cola.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 < μ2 H1 : μ1 - μ2 < 0

This is a left tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 530

x2 = 553

s1 = 23

s2 = 16

n1 = 10

n2 = 10

t = (530 - 533)/√(23²/10 + 16²/10)

t = - 2.6

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [23²/10 + 16²/10]²/[(1/10 - 1)(23²/10)² + (1/10 - 1)(16²/10)²] = 6162.25/383.752

df = 16

We would determine the probability value from the t test calculator. It becomes

p value = 0.0097

Since alpha, 0.05 > than the p value, 0.0097, then we would reject the null hypothesis. Therefore, at 5% significance level, the data suggests that the extra carbonation of cola results in a higher average compression strength.

4 0

3 years ago